I'm gonna' give this a whirl alright. So the equation of a circle is:

differentiating:

or:

or parametrically:

and thus:

Also, you've got to get Mathematica or something else and just plot these to see globally what's happening. In Mathematica 7, you could use:

StreamPlot[{-x,y},{x,-3,3},{y,-3,3}]

ain't that simple or what?